Neural Solvers for Fast and Accurate Numerical Optimal Control

FATROP：一种用于机器人轨迹优化与控制的快速约束最优控制问题求解器

FATROP : A Fast Constrained Optimal Control Problem Solver for Robot Trajectory Optimization and Control

本文提出快速轨迹优化求解器 Fatrop，通过集成基于 Riccati 递归的专用线性求解器并支持阶段式等式约束，兼顾了求解速度与通用非线性求解器的鲁棒性，在毫秒级内解决多种机器人轨迹生成问题并开源。

Gotta Go Fast When Generating Data with Score-Based Models

Score-based (denoising diffusion) generative models have recently gained a lot of success in generating realistic and diverse data. These approaches define a forward diffusion process for transforming data to noise and generate data by reversing it (thereby going from noise to data). Unfortunately, current score-based models generate data very slowly due to the sheer number of score network evaluations required by numerical SDE solvers. In this work, we aim to accelerate this process by devising a more efficient SDE solver. Existing approaches rely on the Euler-Maruyama (EM) solver, which uses…

A Fast Robust Numerical Continuation Solver to a Two-Dimensional Spectral Estimation Problem

This paper presents a fast algorithm to solve a spectral estimation problem for two-dimensional random fields. The latter is formulated as a convex optimization problem with the Itakura-Saito pseudodistance as the objective function subject to the constraints of moment equations. We exploit the structure of the Hessian of the dual objective function in order to make possible a fast Newton solver. Then we incorporate the Newton solver to a predictor-corrector numerical continuation method which is able to produce a parametrized family of solutions to the moment equations. We have performed two …

A Simple and Fast Coordinate-Descent Augmented-Lagrangian Solver for Model Predictive Control

This paper proposes a novel Coordinate-Descent Augmented-Lagrangian (CDAL) solver for linear, possibly parameter-varying, model predictive control (MPC) problems. At each iteration, an augmented Lagrangian (AL) subproblem is solved by coordinate descent (CD), exploiting the structure of the MPC problem. The CDAL solver enjoys three main properties: (i) it is construction-free, in that it avoids explicitly constructing the quadratic programming (QP) problem associated with MPC; (ii) is matrix-free, as it avoids multiplications and factorizations of matrices; and (iii) is library-free, as it can…

PRESAS: Block-Structured Preconditioning of Iterative Solvers within a Primal Active-Set Method for fast MPC

Model predictive control (MPC) for linear dynamical systems requires solving an optimal control structured quadratic program (QP) at each sampling instant. This paper proposes a primal active-set strategy (PRESAS) for the efficient solution of such block-sparse QPs, based on a preconditioned iterative solver to compute the search direction in each iteration. Rank-one factorization updates of the preconditioner result in a per-iteration computational complexity of $\mathcal{O}(N m^2)$, where $m$ denotes the number of state and control variables and $N$ the number of control intervals. Three dif…

Fast Iterative Solver for the Optimal Control of Time-Dependent PDEs with Crank-Nicolson Discretization in Time

In this article, we derive a new, fast, and robust preconditioned iterative solution strategy for the all-at-once solution of optimal control problems with time-dependent PDEs as constraints, including the heat equation and the non-steady convection--diffusion equation. After applying an optimize-then-discretize approach, one is faced with continuous first-order optimality conditions consisting of a coupled system of PDEs. As opposed to most work in preconditioning the resulting discretized systems, where a (first-order accurate) backward Euler method is used for the discretization of the time…